Hello everyone. I just don't get this . This seems very basic but I have problems to find a answer to this. I know augmented matrices and gaussian elimination.

Ok once again Ax = b

Okay I get the augmented matrix form. But how can I do this "backwards"

A is 2x2 matrix , and

x =[0;

3]

b = Null vector

if A was [a,b;c,d] then I came up with 3c + 3d = 0 and then set c =1 ,d=-1

This didn't function

At the moment I am incapable of coming up with a matrix which certain vectors are in the kernel or image. I can't make a matrix which needs to have certain solutions.